Hi, please help I am stuck on this one. I think the surface is that of a sphere or something like that but I cannot work out the above/below equation.
r(u,v) = (cos u sin v, cos u cos v, sin u)
I know that you guys dont like to just give the answers without the poster even trying, so here is what I have so far:
If the problem is: r(u,v) =(cos u sin v, cos u cos v, sinu) as above, then the non-parametric equation looks like the form:
F(x,y,z) = C where F is a function of the x,y,z coordinates defining the sphere and C is 1 so that it is completely spherical? i think... like x^2, y^2, z^2 = 1
Can anyone help make this a non-parametric equation?
edit. Actually x^2+y^2+z^2 =1 is right isnt it? But what is the algebra to derive this?
Cheers!
ok,
I know that it needs some algebraic manipulation, but I dont know how to do it with sin/cos. like can you show me the first 1 please?
I can only get this far:
x^2= cos^2u sin^2v
cos^2u=x^2-sin^2V
u=x^2-sin^2v-cos^2
y^2= cos^2u cos^2v
cos^2u=y^2-cos^2v
u=y^2-cos^2v-cos^2
z^2= sin^2u
sin^2u=-z^2
u=-z^2-sin^2
arggghhh... dun even know what im doing!
ok wait a min...
Assuming its a unit sphere (This assumption seems wrong to lead to making a solution.. but anyway..)
For a unit sphere: (x, y, z) = r(u,v)
= (u,v, root of 1-u^2-v^2)
if u=x, and v=y, and z=1-x^2-y^2
simplified to: z^2=1-x^2-y^2
then x^2+y^2+z^2=1 And thats the solution according to my answer sheet.
However, how do I answer the problem correctly...given that x,y,z are defined through cos/sin vectors.
There is an interm step x^2 + y^2 = cos^2u in the solution sheet i got, but I dont understand how it got to that point